American Educational Research Association

Telling Identities: In Search of an Analytic Tool for Investigating Learning as a Culturally Shaped Activity Author(s): Anna Sfard and Anna Prusak Source: Educational Researcher, Vol. 34, No. 4 (May, 2005), pp. 14-22 Published by: American Educational Research Association Stable URL: http://www.jstor.org/stable/3699942 Accessed: 04/12/2009 10:40 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=aera. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected].

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Telling Identities: In Search of an Analytic Tool for Investigating Learning as a Culturally Shaped Activity by Anna Sfardand Anna Prusak Inthis article,the authors makean attemptto operationalizethe notion of identityto justifythe claim about its potential as an analytic tool for investigatinglearning.They define identityas a set of reifying, significant,endorsable stories about a person. These stories, even if individuallytold, are products of a collective storytelling.The authors' mainclaimis that learningmaybe thoughtof as closingthe gap between actualidentityand designatedidentity,two sets of reifyingsignificant stories about the learner that are also endorsed by the learner.Empiricalillustrationcomes from a study in whichthe mathematicallearningpractices of a group of 17-year-oldimmigrantstudents from the former Soviet Union, newly arrived in Israel,were comparedwith those of native Israelis.

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days, the term identity is prominent in both schol-

arly and public discourses. The time-honored notion is experiencing an obvious renaissance, with its comeback even more impressive than its original appearance. Once a part of specialized psychological vocabularies, it now enjoys the attention of researchersin a wide range of social and humanistic sciences, including sociology, cultural studies, anthropology, and history. Educational research is no exception. As aptly stated by Diane Hoffman, "Identity has become the bread and butter of our educational diet" (Hoffman, 1998, p. 324). This article is devoted to reflections on the emerging educational discourse on identity. We focus on the reasons for its current popularity, on its present shortcomings, and on the conceptual work that has yet to be done before the notion of identity can fulfill its promise as an "analyticlens for educational research"(Gee, 2001). The decision to engage in this conceptual debate has been spurred by our own experience. While reflecting on the results of the recent empirical study in which the mathematical learning practices of a group of 17-year-old immigrant students from the former Soviet Union were compared with those of native Israelis (Prusak, 2003), we opted for speaking in terms of identity to make sense of salient differences between the two groups. And yet, after many hours spent in libraries and on the Web, we concluded that we would not be successful unless we came up with a definition of identity more operational than those to be found in the current literature. Lengthy deliberations EducationalResearcher,Vol. 34, No. 4, pp. 14-22

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led us to the decision to equate identities with storiesabout persons. No, no mistake here: We did not say that identities were finding their expressionin stories-we said they were stories. In what follows, we precede the more detailed presentation of this definition and its subsequent justification with an analysis of the reasons for our dissatisfaction with other current approaches. Later,we argue that the narrativerendering of identity, while not as "reductionist"as it may sound, leads to immediate theoretical insights inspired by the burgeoning researchon human communication. Finally, we use our own cross-cultural study on learning to demonstrate that equating identities with stories makes the notion well suited to its designated role as a tool for educational research. While doing all of this, we do not aspire to say what has not been alreadysaid, or at least hinted at, by others. Rather,we wish to make things more explicit and fully operational, so as to be able to use the language of identity in a responsible way, while following the theoretical consequences of this use all way down. At present such action seems to be urgently needed. Far-reaching ramifications of the identity upheaval may easily be overlooked because our language tends to resist innovations. Because of their transparency, vocabularies and grammars refuse to lend themselves in a timely manner to our attempts to de-familiarizethe familiar. To be able to address conceptual pitfalls that are likely to arisewhen new ideas are already under way but the old ones have not yet disappeared,we have to pause for a moment and turn our attention to the discourse itself.

Defining Identity as Narrative Why Talk About Identity? The new prominence of the old concept of identity raises many questions: Why this sudden revivalof the long-standing interest? How is the notion of identity different from more traditional terms, such as character,nature,andpersonality,and how is it connected to other notions, such as attitudes,conceptions,and beliefs? Why one needs identity depends on the researcher'squestions, and these questions may not be the same for a sociologist, a cultural theorist, and an educational researcher. This said, all of these types of researchhave one overarching theme in common: The focus of the investigator's attention is on human beings in action and on the mechanisms underlying human action. More specifically, the leading queries are as follows: Why do different individuals act differentlyin the same situations?And why, differencesnotwithstanding,do differentindividuals'actions oftenreveal a distinctfamily resemblance?

It is reasonableto assumethatthe presenttendencyto answer the latterquestionin termsof identityis relatedto the general socioculturalturnin the humansciences.The notionsofpersonality, character,and nature,being irrevocablytaintedwith connotationsof naturalgivensand biologicaldeterminants,are ill suitedto the socioculturalproject.In contrast,identity,which is thoughtof as man-madeandasconstantlycreatedandre-created in interactionsbetweenpeople(Holland& Lave,2003; Bauman, 1996; Roth,2004), seemsperfectforthe task.Togetherwith the acceptanceof identityas the pivotalnotion of the new research discoursecomes the declarationthat human beings are active agentswho playdecisiverolesin determiningthe dynamicsof social life and in shapingindividualactivities. Naturally,thisemancipatory messagedoesnot comewithouta The freer we are to make decisions aboutourselvesand the price: worldsaroundus, the greaterour responsibility. In sociologyand in culturaltheory,the notionof identityproveshelpfulin dealing with issuesof powerandof personalandcollectiveresponsibilities for individuallives. In particular,identityfeaturesprominently wheneverone addressesthe questionof how collectivediscourses shapepersonalworldsandhow individualvoicescombineinto the voiceof a community.In thiscontext,the termidentijyingisto be understoodasthe activityin whichone usescommonresourcesto createa unique,individuallytailoredcombination. The questionof the mechanismsthroughwhich the collective and the common enter individualactivitiesalso lies at the centerof educationalresearchon learning.Cross-culturaland cross-situationalinvestigationson what and how people know as a resultof learninghavefurnishedampleevidencefor the existence of culturaldifferences(on mathematicallearning,see, e.g., Lave,1988; Saxe, 1991; Nunes, Schliemann,& Carracher, 1993; Beach, 1995; Cole, 1996; Stigler& Hiebert, 1999; Ma, 1999). Accordingto John Ogbu (1992), "[w]hatthe children bringto school-their communities'culturalmodelsof understandingof "socialrealities"and the educationalstrategiesthat they, theirfamilies,and theircommunitiesuse or do not use in seekingeducationareasimportantaswithin-schoolfactors"(p. 5). This said,educationalresearchhasyet a long way to go beforeit answersthe questionof howthe culturalshapingof learningtakes place.While speakingabout "culturalproductionof educated person,"Levinsonand Holland (1996) observedthat in spite of the recentadvancesin the researchon learning,culturaldiversity, and equity,the "deeper,structuralcontext of culturalproduction of schoolfailureremainedobscureandlargelyunaddressed" (p. 8). The same can be said about the productionof success, which was the focus of Ann Prusak's(2003) study.Her interest in the questionof how the broadlyconceivedsocioculturalcontextaffectsindividuallearningwasoccasionedby the recentmassiveimmigrationfromthe formerSovietUnion to Israel.1More specifically,it was triggeredby a spontaneous,yet-to-be-tested observationthat a disproportionately largesegmentof this particulargroupof immigrantscould prideitself on impressiveresultsin mathematics,and not just in school but alsoin national and internationalmathematicalcompetitions.2The researcher beganaskingherselfwhethertherewas anythingunique about the immigrantstudents'mathematicslearningand if therewas, how this uniquenesscould be accountedfor.

We believethat the notion of identityis a perfectcandidate for the role of "themissinglink"in the researchers' storyof the complexdialecticbetweenlearningandits socioculturalcontext. We thus concurwith the increasinglypopularidea of replacing the traditionaldiscourseon schoolingwith the talkabout"constructionof identities"(Lave& Wenger, 1991, p. 53) or about the "longer-termagendaof identitybuilding"(Lemke,2000; cf. Nasir & Saxe,2003). And yet we also believethat the notion of identitycannotbecometrulyusefulunlessit is providedwith an operationaldefinition. What Is Missing in the CurrentEducational Discourseon Identity? As preparationfor the criticalanalysisof the currentdiscourse on identity, it may be useful to give thought to certainwelldocumented weaknessesof widely used motivationalnotions suchas beliefior attitudeswhich, on theirface,can competewith identityfor the role of conceptualbridgebetweenlearningand its culturalsetting. Fundamentalobjectionsto the notion of beliefwereraisedby manywriters,notablyby Geertz(1973), who assertedthe unacceptabilityof this conceptwhen claimingthat it "[married]extremesubjectivism to extremeformalism,withthe expectedresult: an explosionof debateas to whetherparticularanalyses... reflectwhat [people]"really"think"(p. 11). The issueat stakewas that of the essentialistvision of beliefs,one that assumedtheir discourse-independentexistencewithout specifyingwhereand how one could get hold of them.A similarcomplaintseemedto underlieHerbertBlumer's"criticalassessmentof the conceptof attitude as a tool for study and analysisof human conduct" (Blumer,1969, p. 90). Accordingto Blumer,whateverone'sapproachto the notionof attitude,thatnotionwasnot operational. That is, it regularlyfailedto meet the threenecessaryconditions for the concept'sapplicabilityin research:The availabledescriptions did not specifywhatone shouldlook at whiletryingto pinpoint attitudes,did not saywhat should not be consideredas a memberof the class,and did not enableaccumulationof knowledge.The immediatereasonforall thesefailingswas,once again, a certainessentialisttenet,namely,"thatthe tendencyto act [precedesand] determinesthat act"(p. 90). As in the caseof belief, the assumptionthat an intention (or tendency)exists in some unspecified"pure"formindependentlyof, andpriorto, a human actionwas a dubiousbasisfor any empiricalstudy. Returningto our theme,we now wish to claimthatthe notion of identity,althoughpromisingandpotentiallybettersuitedto the roleof a "toolforthestudyof humanconduct,"cannotbe declared freefromsimilarweaknessesunlessits definitionis spelledout and provedoperational.Sucha definitionhasyet to be found.In the currentliteraturethe useof the wordidentityis rarelyprecededby any explanations.In the absenceof a definition,the readeris led to believethat identityis one of those self-evidentnotions that, whetherreflectively or instinctively,arisefromone'sfirsthand,unmediatedexperience.The influentialpublicationsby Laveandby in thisrespect.Althoughidentityis one Wengerarerepresentative of thesewriters'pivotalideas,no conceptualpreparations precede sentencessuchas "Learning ... impliesbecominga differentperson [and]involvesthe constructionof identity"(Lave& Wenger, 1991, p. 53), or "Theexperienceof identityin practiceis a way of beingin the world"(Wenger,1998, p. 151).

A few defining attempts that can be found in the recent literature may be a promising beginning. For instance, Gee (2001) says: "Being recognized as a certain 'kind ofperson,' in a given context, is what I mean ... by 'identity"' (p. 99, italics added). Later, the author offers a more elaborate description: Discoursescangiveus one wayto definewhatI calledearliera person's "coreidentity."Each person has had a unique trajectory through"Discursivespace."Thatis, he or shehas,throughtime,in a certainorder,had specificexperienceswithin specificdiscourses (i.e., been recognized,at a time and place, one way and not another),some recurringandothersnot. This trajectoryand the person'sown narrativization (Mishler,2000) of it arewhatconstitute his or her(neverfullyformedor alwayspotentiallychanging)"core identity."(p. 111) The motif of a "person's own narrativization"recurs in the description proposed by Holland, Lachicotte, Skinner, and Cain (1998), even if formulated in different terms: People tell otherswho they are,but even more importantly,they tell themselvesand they tryto act as thoughthey arewho theysay they are.These self-understandings, especiallythose with strong emotionalresonancefor the teller,arewhat we referto as identities. (p. 3) If we said that these are "promising beginnings" rather than fully satisfactory definitions, this is because of one feature common to them all: They rely on the expression "who one is" or its equivalents. Even Gee's second offering cannot be understood without it: The words "being a certain kind of person" are used in the author's explanation of the term Discourse,which is pivotal to his second definition.3 Unfortunately, neither Gee nor Holland and her colleagues make it clear how one can decide "who" or "what kind of person" a given individual is. With closer examination, the talk about "being a certain kind of person" may be pushing us into precisely the trap that most of the authors who use the notion of identity want to escape: Through its very syntax, the expression implies that one's present status is, in a sense, extra-discursiveand independent of the one's actions. Sentences built around the idea of "being a kind of person" sound timeless and agentless. As such, these sentences seem to be saying that there is a thing beyond one's actions that stays the same when the actions occur, and also that there is a thing beyond discourse that remains unchanged, whoever is talking about it. Such an essentialist vision of identity is as untenable as it is harmful. It is untenable because it leaves us without a clue as to where we are supposed to look for this elusive "essence"that remains the same throughout person's actions. It is potentially harmful because the reified version of one's former actions that comes in the form of nouns or adjectives describing this person's "identity" acts as a self-fulfilling prophecy. As agents of continuity and perpetuation, the descriptors that outlast action exclude and disable just as much as they enable and create (Ben-Yehuda, Lavy, Linchevski, & Sfard, 2003).4 Although contrary to the intentions of the authors quoted above, these interpretations cannot be barredas long as the words "being a kind of person"remain the centerpiece of the definition of identity. The question we are now facing is how to define identity so as to make the notion operational, immune to undesirable connotations, and in tune with 161 EDUCATIONALRESEARCHER

the claim about identities as man-made and collectively shaped rather than given. How to Define Identity? The definitions of identity set forth by Gee and Holland et al., although rather unlikely to pass Blumer's test of admissibility, have an important insight to offer: By foregrounding the "person's own narrativizations"and "telling who one is," they link the notion of identity to the activity of communication, conceived broadly as including self-dialogue-that is, thinking. Together with many others (e.g. Hall 1996; Gee, 2001; Gonzales, 1999), we readily embrace the idea of identity-making as a communicational practice and thereby reject the notion of identities as extra-discursive entities that one merely "represents"or "describes"while talking. Perhaps the most obvious identifying technique consists in replacing the talk about actions with talk about states or, more specifically, in replacing utterances about doingwith reifying sentences about being or having.5The reifying effect follows directly from the particular syntax of the "is-sentences,"such as She is an able student (has a gift). This brief proposition can be "unpacked" into the following sentence: In the majority of school tests and activities so far, she has regularlydone well and attained above-averagescores. In modern societies we have an unbounded arrayof institutional means for describing "who one is": We do it with the help of grades, test results, certificates, passports, diagnoses, licenses, diplomas, titles, ranks-and this is just the beginning of the long list. In fact, almost any social situation seems to be a good opportunity for reifying. Why this overpowering proclivity for "is-sentences"?Paradoxically, the reason may be exactly the same as the one that formerly evoked our concern: We cannot do without the is-sentences because of their reifying quality. Our relations with the world and with other people change continually, sensitive to our every action. Metaphorically speaking, identifying is an attempt to overcome the fluidity of change by collapsing a video clip into a snapshot. The use of is-sentences, which do the job of "freezing the picture" and turning properties of actions into properties of actors, is grounded in the experience-engendered expectationindeed, hope-that despite the process of change, much of what we see now will repeat itself in a similar situation tomorrow. Based of this assumption, identity talk makesus able to copewith new situations in termsof our past experienceand gives us tools to plan for thefiture. In concert with the vision of identifying as a discursive activity, we suggest that identities may be defined as collections of stories about persons or, more specifically, as those narrativesabout individuals that are reifying,endorsable,and significant.The reifying quality comes with the use of verbs such as be, have or can rather than do, and with the adverbs always, never, usually, and so forth, that stress repetitiveness of actions. A story about a person counts as endorsable if the identity-builder, when asked, would say that it faithfully reflects the state of affairsin the world. A narrativeis regardedas significantif any change in it is likely to

affectthe storyteller'sfeelingsabout the identifiedperson.The most significantstoriesare often those that imply one's membershipsin, or exclusionsfrom,variouscommunities. As a narrative,everyidentifyingstorymay be representedby the tripleBAC,whereA is the identifiedperson,B is the author, and C the recipient.Within this renderingit becomesclearthat multipleidentitiesexistfor anyperson.Storiesabouta givenindividualmay be quite differentfrom one another,sometimes even contradictory.Althoughunifiedby a familyresemblance, theydependboth in theirdetailsand in theirgeneralpurporton who is tellingthe storyandforwhom the storyis intended.What a personendorsesas true about herselfmay be not what others see enacted.To ensurethatthislastpoint would neverdisappear fromour eyes,we distinguishedbetweenan individual'svarious identitiesauthoredby differentpeople with the help of names that indicatethe relationbetweenthe identifiedperson,the storyteller,and the recipient. AAC = an identifyingstory told by the identifiedpersonherself.This storywe callA'sfirst-person identity(1st P). BAA= an identifyingstorytold to the identifiedperson.This identity(2nd P). storywe callA's second-person BAc= a story aboutA told by a third partyto a third party. This story we call A's th,ird-person identity (3rd P)

Among these, thereis one specialidentitythat comprisesthe reifying,endorsable,significant1st P storiesthat the storyteller It is this last type of storythat is usuaddressesto herself(AAA). the when word intended identityis used unassistedby addially tional specifications.Being a partof our ongoing conversation with ourselves,the first-personself-told identitiesare likely to havethe most immediateimpacton our actions. WhatAre the Merits and PossiblePitfalls of the Narrative-DefinedIdentity? With the narrativedefinition,human agencyand the dynamic natureof identityarebroughtto the fore, and most of the disof traditionalapproaches seemto disappear.The focus advantages of the researcher's attentionis now on thingssaidby identifiers, and no essentialistclaims are made about narrativesas mere "windows"to an intangible,indefinableentity.As stories,identities are human-madeand not God-given,they have authors and recipients,they are collectivelyshapedeven if individually told, and they can changeaccordingto the authors'and recipients' perceptionsand needs.As discursiveconstructs,they are alsoreasonablyaccessibleand investigable. Despite these obvious advantages,one may claim that "reunderminesits potentialasa senseducing"identityto narratives a is tool. but text,the criticwouldsay,and identity Story making is predominantlyan experience.Perhapsthe most outspoken proponentof this positionis Wenger(1998), who saysthatidentity "isnot, in its essence,discursiveor reflective."And he adds: "Weoften think about our identitiesas self-imagesbecausewe talkaboutourselvesand eachother-and eventhink aboutourselvesandeachother-in words.Thesewordsareimportant,no doubt, but they arenot the full, lived experienceof engagement in practice"(p. 151). Althoughwe agreethat identitiesoriginatein daily activities and in the "experienceof engagement,"it would be a category mistaketo claim that this fact disqualifiesour narrativerender-

ing of identity.Indeed,it is our visionof our own or otherpeople's experiences,and not the experiencesas such, that constitutesidentities.Ratherthanviewingidentitiesasentitiesresiding in the worlditself,our narrativedefinitionpresentsthem as discursivecounterparts of one's lived experiences.(That said, it is importantto stressthat we do not claim that identities"faithfully recount"the identity-engenderingexperiences;together with Wittgenstein (1953), we considerthe very idea of "conveying an experience"to be not only unworkablebut also conceptuallyuntenable.) Furthermore,while we readilyadmit that some very realexperiencespromptpeople to say that they havea "senseof identity,"we alsowish to reversethe causalrelationimpliedby such a saying:We claim that the experiencethat one describesas a "senseof identity"is not the primarysourceof identifyingstorytellingbut ratheris that activity'snaturaloutcome.The ubiquity and repetitivenessof identifying narrativesone tells and hearsaboutherselfmakethem so familiarand self-evidentto her that she eventuallybecomesable to endorseor rejectnew statementsabouther in a direct,nonreflectiveway. Suchimmediacy is necessaryto makeone cerof decision,whenno rationalization of the tain of one'schoices,is the generaldefiningcharacteristic situationsin wnich peoplesaythat they have "asenseor something.In the caseof decisionsregardingphysicalactivity,thisimmediacyresultsfromthe familiaritywith the materialobjectson which the actionsareperformed.Thus, for example,one claims having "a good sense of a terrain"if he is able to find his way througha givenphysicalspacein an instant,"withoutthinking." The use of the expression"senseof' in conjunctionwith "identity"is an act of metaphoricalprojectioninto a discourseon experiencesthatcannotbe accountedfor by a referenceto material objects.The phrasecomes to this latterdiscoursetogetherwith all its objectifyingentailments:The implieddichotomybetween the "sense"and its objectmakesone believein the existenceof the entitycalled"identity"andin its primacyoverthe experience of immediacy,familiarity,and directrecognitionthat accompanies this person'sidentifyingstorytelling. Anotherquestionto explorewhileassessingthe proposeddefinition is whetherour narrative-defined identitycan be usefulin do not researchin spiteof the factthatdifferentidentity-builders self-referential remarks alwaystell the samestory.Indeed,actors' maybe at oddswith thosemadeby an observerandmayvarydependingon the listener,sometimescontradictinga versionpresentedby, or to, somebodyelse (adjustingone'sstoryto listeners is not a sign of insinceritybut ratherstemsfromthe needfor solidarityand effectivecommunication).Let us thus clarifythat it is the activityof identifyingratherthanits end productthat is of interestto the researcher.In studiesthatmakeuse of the notion, the focus is not on identitiesas such but ratheron the complex dialecticbetweenidentity-buildingand other humanactivities. Thus, while lettingourselvesbe guidedby the narrativevision of identity,we arenot afraidof missinganythingthatis "outthere" or of not being able to pin down the "truereferent"of the term "identity."Narrativesthatconstituteone'sidentity,beingan important factor in shaping this person's actions, will be useful in

researchevenif theycommunicateone'sexperiencesonly aswell as humanwordscan tell.

Toward a Narrative Theory of Identity Becausequestions about identity can now be translatedinto andbecausethe dynamqueriesaboutthe dynamicsof narratives, areamenableto empiricalstudy,the narrativedeics of narratives finition may be expectedto catalyzea rich theory of identity. Much can now be said about identitiessimply by drawingon what is known abouthuman communicationand on how narrativesinteractone with another.In this sectionwe presentsome initial,analyticallyderivedthoughtson how identitiescomeinto being and develop. Actual and DesignatedIdentities The reifying,significantnarrativesabout a personcan be split into two subsets:actualidentity,consistingof storiesabout the actualstateof affairs,anddesignated identity,consistingof narrativespresentinga stateof affairswhich,forone reasonor another, is expectedto be the case, if not now then in the future.Actual identitiesusuallyaretold in presenttenseand formulatedas factualassertions.Statementssuch as "Iam a good driver,""Ihave an averageIQ," and "I am armyofficer"are representativeexamples.Designatedidentitiesarestoriesbelievedto havethe potential to become a part of one's actualidentity. They can be recognizedby their use of the futuretense or of wordsthat expresswish, commitment,obligation,or necessity,suchasshould, ought,haveto, must,want,can, cannot,and so forth.Narratives such as "Iwant to be a doctor"or "Ihaveto be a betterperson" aretypicalof designatedidentities. The scenariosthatconstitutedesignatedidentitiesarenot necessarilydesiredbut alwaysareperceivedas binding.One mayexpect to "becomea certaintype of person,"that is, to havesome storiesapplicableto oneself,forvariousreasons:becausethe person thinksthatwhat thesestoriesaretellingis good for her, becausethese are the kinds of storiesthat seem appropriatefor a personof her socioculturalorigins,or just becausethey present the kindof futurethatshe is designatedto haveaccordingto others,in particularaccordingto peoplein the positionof authority and power.Moreoften than not, however,designatedidentities arenot a matterof deliberaterationalchoice.A personmay be led to endorsecertainnarrativesabout herselfwithout realizing that theseare"juststories"and that therearealternatives. Designatedidentitiesgive directionto one's actionsand influenceone's deedsto a greatextent,sometimesin waysthat escapeany rationalization.Forexample,a personfor whom being a Democratis a partof herdesignatedidentitymayrefuseto join any activityinitiatedby Republicans,regardlessof the natureor rationaleof the activity.Foreveryperson,some kindsof stories have more impact than some others. Criticalstoriesare those core elementsthat, if changed,would makeone feel as if one's whole identity had changed:The person's"senseof identity" would be shakenand she would lose her ability to determine, in an immediate,decisivemanner,which storiesaboutherwere endorsableand which were not. A perceivedpersistentgap between actualand designatedidentities,especiallyif it involves criticalelements,is likelyto generatea senseof unhappiness. WhereDo DesignatedIdentities ComeFrom? The Role of SignificantNarrators Becauseit is a narrative,the designatedidentity,althoughprobably more inert and less context-dependentthan actualidentiil| EDUCATIONALRESEARCHER

ties, is neitherinborn nor entirelyimmutable.Like any other story,it is createdfrom narrativesthat arefloatingaround.One individualcannotcount as the sole authoreven of those stories that sound as if nobodyhas told them before. To put it differently, identities are products of discursive diffusion-of our proclivityto recyclestripsof things said by otherseven if we areunawareof these texts'origins.Paraphrasing MikhailBakhtin,we maysaythat any narrativerevealsto us storiesof others.6Identitiescomingfromdifferentnarratorsand beingaddressedto differentaudiencesarein constantinteraction and feed one into another.These storieswould not be effective in theirrelation-shaping taskif not for theirpowerto contribute to the addressees'own narrativesabout themselvesand about others.Thus the people to whom our storiesaretold, as well as those who tell storiesabout us, may be tacit co-authorsof our own designatedidentities.Eitherby animatingotherspeakersor by convertingtheir storiesabout us to the first person,we incorporateour second- and third-personidentitiesinto our selfaddresseddesignatedidentities. Anotherimportantsourcesof one's own identityare stories aboutothers.Therearemanypossiblereasonsfor turningthem into first-personnarrativesand incorporatingthem into one's own designatedidentity.Thus, for example,the identity-builder or to their maybe attractedeitherto the heroesof thesenarratives authors.Anotherreasonmay be one's convictionabout being "made"in the imageof a certainperson(e.g.,of sociallydeprived successfulmother) parents,an alcoholicfather,or an academically and "doomed"to a similarlife. Whethera storytold by somebody else does or does not make it into one's own designated identity depends,among other things, on how significantthe storytelleris in the eyesof the identifiedperson.Significantnarrators,the ownersof the most influentialvoices, arecarriersof thoseculturalmessagesthatwill havethe greatestimpacton one's actions.

How Do DesignatedIdentitiesDevelop and Change? The Role of Narrative Diffusion The fact that narrativesauthoredby othersareamongthe most importantsourcesof our designatedidentities is perhapsthe main reasonfor the relativeinertnessof these identities.Stories once told tend to acquirea life of theirown and, while "changing hands,"stop being subjectto either their author'sor their hero'screativeinterventions.Changingdesignatedidentitiesthat havebeen formedin childhoodis a particularlydifficulttask. Institutional"narratives" suchas diagnoses,certificates,nomand licenses inations, diplomas, (compare Gee's concept of Gee have a I-identity; 2001) particular capacityto supplantstories that havebeen a partof one's designatedidentity.In addition, althoughnarrativeosmosisgoes mainlyfrom designatedto actual identities,one cannot exclude the possibilityof influence thattravelsin the oppositedirection.As impliedby the common wisdom that "successbegetssuccessand failurebegetsfailure," storiesof victoriesand losseshavea particulartendencytoward self-perpetuation.On theirway into designatedidentities,tales of one's repeatedsuccessarelikelyto reincarnateinto storiesof special"aptitude,""gift,"or "talent,"whereasthoseof repeated failureevolve into motifs of"slowness," incapacity,"or even "permanent disability."

Learningas Closingthe Gap BetweenActual and DesignatedIdentities It is now not unreasonableto conjecturethat identitiesarecrucialto learning.Withtheirtendencyto actasself-fulfilling prophecies, identitiesare likely to play a criticalrole in determining whetherthe processof learningwill endwith whatcountsassuccessor with what is regardedas failure. And thereis more. In these times of incessantchange,when the pervasivefluidity of social membershipsand of identities themselvesis a constantsourceof fearand insecurity,the role of learningin shapingidentitiesmaybe greaterthanever.Unlike a few centuriesago,when peoplewereborninto "whotheywere," everythingnow seemspossible.Only insufficienciesof imagination may accountfor the down-to-earthnatureof the majority of storiesabout"whoone is supposedto be." Learningis ourprimarymeansformakingrealityin the image of fantasies.The objectof learningmay be the craftof cooking, the artof appearingin media,or the skillof solvingmathematicalproblems,dependingon whatcountsas criticalto one'sidentity. Whateverthe case,learningis often the only hope for those who wish to close a criticalgap betweentheir actualand designatedidentities. Applying Identity as the "The Missing Link" Between Learning and Its Sociocultural Context In the remainderof this article,we put the narrative-defined identity to work in an attempt to check whether it fulfills its promiseas a tool for fathomingthe mechanismthroughwhich the widercommunity,with its distinctcultural-discursive traditions, impingeson its members'learning.This is done in the contextof the study that involvednativeand immigrantIsraeli mathematicsstudents.In whatfollows,we presentan "executive summary"of severalhighlightsof this study (the full reportcan be found in Prusak,2003). The Study and Its Initial Findings The researchprojectfocused on one 1 th-gradeclassthat followed an advancedmathematicsprogram.Nine of the 19 studentswere"NewComers"-recentimmigrantsfrombig citiesin the formerSovietUnion, suchasMoscow,Kiev,andTbilisi.The restwere nativeIsraelis,whom we call "OldTimers."All of the studentscamefromwell-educatedfamilies.The secondauthor, a one-time immigrantfrom the Soviet Union, served as the teacher.In the courseof the entire 1998-1999 school year,all classroomprocessesweremeticulouslyobservedanddocumented. Numerousinterviewswith the students,theirparents,and other teachersconstitutedadditionaldata. The salienceof the differencesbetweenthe learningprocesses of the two groupsexceededour expectations.We were also astonished by the strikingacross-tasksconsistencyof the intragroup homogeneityand of the inter-groupdisparities.For the sakeof brevity,in the restof this reportwe will drawon just two special cases that we regardas fully representativeof the two groups:the casesof one OldTimerand one NewComer,whom we shallcall Leahand Sonya,respectively. Although, accordingto common measures,both girls could be deemed successfulin their mathematicallearning,they differedsubstantiallyin the way that theylearned.Thus, for exam-

ple,whilestudyingindependentlywith thehelpof a textbookand a worksheet,Leahtypicallyexecutedall the auxiliarytasksspecifiedby the teacherandwascarefulto producewrittenevidenceof thiswork.Sonya,in contrast,did not botherto leaveanyrecords of what she did. On the other hand, her self-reportsrevealeda much more complexprocessof learning,one that includedrepeatedself-testing,self-correcting,and attemptsat finding her own organizationof the learnedmaterial.Clearly,whatevershe did in the courseof learningwasdoneforherself,accordingto her own assessmentof its importance.For Leah,the teacherseemed to be the ultimateaddressee. These and numeroussimilarobservationsled us to the conclusion that Leah'slearningwas ritualized-that is, motivated mainlyby a wish to adhereto the rulesof the gamewith which, for social reasons,she felt obliged to comply. Her learningwas thoughtof asan activitywhoseimportanceresidedin its veryperformance.In contrast,Sonyastrovetowardsubstantial learninglearningwhose effects would outlast classroomactivitiesand could be gaugedaccordingto criteriaindependentof the tastes or personalopinionsof a particularteacher.Sonya'swish to attain lastingeffectscould be observedthroughoutour extensive studyand was evidencedby her constantbacktrackingand selfexamination,by herconspicuouspreferencefor individualwork, of her mathematicalexpresby her carefor the appropriateness sion, andmoregenerally,by herinsistenceon followingall of the rulesof communicationthat, accordingto her own assessment (as opposedto that of the teacher,for example),could count as genuinely"mathematical." Not surprisingly, thereseemedto be a tightcorrespondence betweenthewaysthatthe two studentslearnedandthe effectiveness of theirlearning.Thus, for example,on one unannouncedtest, Sonyawas fully successfulin reproducingthe proof, which she hadlearnedon herown a few daysearlier.In contrast,Leahfailed even to formulatethe theorem (admittedly,this failurewas an extremeevent in her school career;her test performanceswere generallyrathersuccessful).Here, as almosteverywhereelse, the two girlswerefullyrepresentative of theirrespectivegroups,both in the waythattheylearnedand in the resultsthatthey attained. Linking Learning to Identity The striking dissimilarities between the OldTimers' and NewComers'learningcalledfor explanation.Althoughwe had a basison which to claimthe existenceof certainsystematicdifferencesin the teachingpracticesin the formerSoviet Union and in Israel,7these differencesdid not seem to tell the whole story.A teachingapproachmight havebeen responsiblefor the NewComers' acquaintancewith certain techniques, but acquaintance,per se, did not accountfor the students'willingness to use those techniques.We felt that, to complete the explanation, we needed to clarifywhy the participantsin our study were among the studentswho took advantageof the learning opportunitiescreatedby their teachers. Yet anotherobvious explanationfor the effectivenessof the NewComers'learningwas that theirimmigrantstatusamplified theirneed for success.8However,becausebeing an immigrantis a part of one's identity, this conjecturebroughtus back to the broaderquestionof how our findingscan be accountedfor on the basisof the claimaboutlearningas closingthe gap between MAY 2005|I9

actualand designatedidentities.This broaderconsiderationwas certainlynecessaryif we wereto explainwhy school mathematics was singledout by the immigrantparticipantsof our study as the mediumthroughwhich to exercisetheirpursuitof excellence. Indeed,no otherimmigrantpopulationin Israel-and Israelhasalwayshadmany-displayed a comparablepropensityfor mathematics. To map NewComers'and OldTimers'designatedidentities, we listened to their stories about themselvesas told to their teacheron variousoccasions.True,what we reallyneededwere

triculatingin thissubjectwith high gradeswould largelyincrease herchancesfor beingacceptedby a university.In otherwords,if Leahwas attractedto mathematics,it was mainly, perhapsexclusively,becauseof its abilityto open doors. To summarize,the designatedidentitiesof Sonyaandherfellow NewComersportrayedtheirheroesas exemplarsof whatthe NewComers themselvesdescribedas "the complete humans." The termwasassumedto havea timeless,universal,generallyacceptedmeaning,which includedmathematicalfluencyas indispensableto the completeness.In contrast,Leah and the other OldTimersexpectedto havetheirfuturelife shapedby theirown self-addressedstories of the type AAArather than AATeacher,because self-addressed storiesaremorelikelyto interactsignificantlywith wishesand needs,which, at the time, they saw as fluid and unone's actions.This preferencenotwithstanding,we were confiforeseeable.This contrastpoints,aswell, to a distinctmeta-level dent thatthe teacher-addressed differencebetweenthe two groups:The NewComerssaw their designatedidentitieswouldprove informative,especiallyif they displayeddiversityparallelingthe highlyprescriptivedesignatedidentitiesas givenand apparently observeddifferencesin learning.In addition,we made certain immutable,preciselylike the mathematicsthey wantedto masdeductionsregardingwhat the NewComersand OldTimersexter,whereasthe OldTimersexpectedtheirfirst-personidentities to evolvewith the worldin tandem. pected of themselves,on the basis of their self-referentialreIn accordwith our expectations,all of this seemedto account, marks,theircommentsabout others(e.g., the teacherof fellow at leastin part,for our formerfindingsabout the differencebestudents),andour own observationsof theirbehavior.Forbacktween Leah'sand Sonya'slearning.Sonya, just like the other groundwe used interviewswith the students'parentsand with otherteachers.Whatwe foundwith the help of thismultifarious NewComers,neededmathematicalfluencyto close the critical evidencedisplayedintra-groupuniformityand inter-groupdifgap betweenher actualand designatedidentities.ForLeahand ferencescomparablein theirsalienceto thoseobservedpreviously the otherOldTimers,mathematicalfluencywassomethingto be in the contextof the students'learning. shownupon request,likean entranceticketthatcouldbe thrown Again,we will exemplifythesefindingswith the representative awayafteruse,havingno valueof its own. Becausemathematical casesof Leahand Sonya.Of necessity,we will followwith some skillsdid not constitutea criticalelementof the OldTimers'desgeneralizations.Becauseof the limitationof space,we will talk ignatedidentities,any absenceor insufficiencyin theirmatheabout what students said ratherthan reproducingtheir exact maticalskillsdid not createsubstantiallearning-fuelling tension. words.Awareof the limitationsof suchan approach,we urgethe Linking Identity to the SocioculturalContextof Learning readerto rememberthatwhat followsis a storyaboutstories:It is Wheredoes the disparitybetweenNewComers'and OldTimers' ourstoryof theNewComers'andOldTimers'own narratives, and designatedidentitiescome from?This was the last questionthat not authorlessassertionsabout"whothesestudentsreallywere." had to addressto completeour storyof designatedidentityas we In other words, ours are stories of the type researchers [AATeacher] readers a link betweenlearningand its sociocultural setting.Morespecifand researchers [AAA]readers) rather than of the type researchersAreaders. we needed to for fact that mathematical account the ically, fluency Probablythe most obviouscriticalelementof Sonya'svision constitutedthe criticalelementof the NewComers'designated of herselfin the futurewasherprofessionalcareer.Her tendency identitiesbut did not seem to playthat role in the identitiesof to identifyherselfmainlyby her designatedprofessionof medOldTimers. ical doctor stood in starkcontrastto Leah'sdeclarationsof her The first thing to say in this context is that, given the need "to be happy"and her adamantrefusalto specifyany conNewComers' creteplansfor the future.The professionsdesiredby Sonyaand immigrantstatus,theirbeingwell versedin mathematics appearedto be of redemptivevalue:The universalityof thosementionedby otherNewComers(e.g., computerscientist, skillswas likelyto constitutean antidoteto these mathematical medicaldoctor, engineer)all were relatedto mathematics,and sense of localexclusion.To stateit in termsof identity, students' this fact appearedto accountfor these students'specialmathethat we conjecture maticalproclivity.Yetthereseemedto be moreto thesestudents' althoughNewComerswereboundto identify as in theirlocalenvironment,mathematical themselves outsiders inclinationfor mathematicsthanjust the wish to promotetheir was one of those prowess propertiesthatcompensatedthemwith professionalprospects.Accordingto the NewComers'frequent more the statusof "peopleof edprestigious,place-independent remarks,the specialattractionof mathematicswasin the factthat ucation and culture."9 its rulescould be seen as universalratherthan specificto a particularplaceor culture.In explainingwhy she choseto learnadClearly, the idea that education at large, and mathematical fluvancedmathematics,Sonya,like the other NewComers,spoke ency in particular, might counterbalance the less advantageous elements of their identity was not the young NewComers' origaboutthe knowledgeof mathematicsas a necessaryconditionfor inal invention. In general, what the participants of our study exher becoming"afully fledgedhumanbeing."We thushavereason to claimthat mathematicalfluencyas such, and not just the pected for themselves was not unlike what their parents and rewardsthat could be expectedto come with it, constitutedthe grandparentswished for them. In both groups this link could be criticalelementin Sonya'sand other NewComers'first-person seen from the students' assertions about the full accord between theirown andtheirparents'expectations,andfromtheirremarks designatedidentities.In contrastLeah,in explainingher choice abouttheirparents'impacton theirchoices.Nevertheless,there of an advancedmathematicscourse,stressedthe fact that ma20 11EDUCATIONAL RESEARCHER

was an important difference between our two populations. The OldTimers' parents, unlike those of the NewComers, were described as willingly limiting the areaof their influence and leaving most decisions about the future in the young people's own hands. We also found it quite telling that parents were rarelymentioned in the OldTimers' autobiographical testimonies, whereas the NewComers' accounts were repletewith statements about their elders' authority and with explicit and implicit assertions regarding the parents' all-important role in their children's education. Obviously, the OldTimers' parents' stories about their children's future were not as prescriptiveas those of the NewComers, nor was the influence of the parents'stories equally significant. Narratives about education as a universal social lever and about knowledge of mathematics as one of the most important ingredients of education evidently constituted a vital part of the NewComers' cultural tradition. In their native countries, their families belonged to the Jewish minority. According to what we were told both by the students and by their parents, these families had typically identified themselves as locally excluded but globally "athome," thanks to their fine education. Their limited sense of attachment to the ambient community was likely the reason for the young people's relative closeness to their families. In the interviews, both the parents and the children sounded fully reconciled to their status of local outsiders. Proud of their cultural background and convinced about its universal value, they seemed to consider this kind of exclusion as the inevitable price for, and thus a sign of, the more prestigious, more global cultural membership. It seems, therefore, that the NewComers' identities as local outsiders who were destined to overcome their exclusion with the help of place-independent cultural assets such as mathematics were shaped by their parents' and grandparents' stories prior to the students' immigration to Israel. Because significant narrators can count as voices of community, all of these findings corroborate the claim that designated identities are products of collective storytelling-of both deliberate molding by others and uncontrollable diffusion of narratives that run in families and communities. This assertion completes our empirical instantiation of the claim that designated identity is "apivot between the social and the individual" aspects of learning (Wenger, 1998, p. 145).

The key move was to equate identity-building with storytelling. The difference between identity as a "thing in the world" and as a discursive construct is subtle. The kind of data that the narrative-minded researcheranalyzes in her studies is the same as everybody else's: These are stories that people tell about themselves or about others to their friends, teachers, parents, children, and bosses, as well as to researchers.The only distinctive feature of the present narrativeapproach is that, ratherthan treat the stories as windows to another entity that stays unchanged when "the stories themselves" evolve, the adherent of the narrativeperspective is interested in the stories as such, accepting them for what they appear to be: words that are taken seriously and that shape one's actions. This scholar-while analyzing the various narratives' incessant co-molding, their dialectic interaction with people's deeds, their flow from one generation to another, and their back-and-forth movement between the community and individual levels-is uniquely positioned to answer the time-honored questions presented in the beginning of this article: Whydo different individuals act diferently in the same situations?And why, diferences notwithstanding, do different individuals' actions often reveala distinctfamily resemblance?

Concluding Remarks: The Promise of the "Narrative Turn"

call a 'Discourse'...

Summarizing her reflections on the delicate trade-off between the advantages and the imperfections of the notions of culture and identity, Norma Gonzales ventured this prediction: "If I were to engage in a prescient attempt to name the direction of future researchin anthropology and education, my bet would be the theory and practice of language ideologies" (Gonzales, 1999, p. 433). One of her reasons for envisioning this particular development was the conviction that the discursive turn would increase the researchabilityof social phenomena: Questions about intrapersonal and interpersonal mechanisms would reincarnate into questions about the dynamics of discourses, which would be helpful, because "people's ideas about language use are readily accessible to researchersand practitioners" (p. 434). In this article, we hope to have started turning this prediction into reality.

NOTES We aregratefulto the anonymousreviewersand to MicheleFosterfor theirinsistent,friendlycriticism,whichhelpedus to makeourargument clearerand morefocused.We alsowish to thankthe 1Ith-grademathematicsstudentswho agreedto participatein ourstudy.A previousversion of this articlewas presentedat the 2004 annual meeting of the AmericanEducationalResearchAssociationin San Diego, CA. 1 Accordingto the leadingIsraelinewspaperHaaretz,"Approximately 200 thousandchildrenimmigratedto Israelin 11 years,most of them fromthe formerSovietUnion;theyconstitute15%of the Israeliyouth" (August 31, 2001). 2 This conjectureshouldnot be misreadas meaningthat immigrants from the formerSovietUnion aregenerallymore successfulin mathematics than the rest of the Israelipopulation.As reportedin Haaretz (August2, 1996), "Thereare [immigrant]childrenwho arriveat the highestplacesin internationalcompetitionsin mathematicsandphysics and thanksto them, Israelclimbedfrom24th to 13th placein the 1995 internationalchampionship." 3 A few pagesearlier(p.110), the authorsaid:"Anycombinationthat can get recognizedas a certain'kind of person'(e.g. a certainkind of AfricanAmerican,radicalfeminist,doctor,patient,skinhead)is what I

with a capital 'd'. ... Discourses are ways of being

'certainkinds of people."' 4 This concernis not unlike the one raisedby Guttirezand Rogoff (2003), who makea caseagainstspeakingin termsof individualtraits andproposethat"individuals' andgroups'experiencein activities-not theirtraits-becomes the focus"of research(p. 19). 5 Throughthe waysthat we talk,we populateour worldswith entities supposedlyoutlastingour actions.With wordswe turn processes into objects,into the "permanententities"to which our actionsareapplied or which resultfrom these actions(Sfard,1991, 1994); it is also with wordsthat we reifythe discursivesubjects-the implementersof the actions. 6 Bakhtin(1999) spokeaboututterancesandwordsratherthanstories. 7 The secondauthorof this study-on the basisof sourcessuchas her personalexperienceasa studentandasa teacherin Belarus,hersurveyof Russianmathematicstextbooks,and her interviewswith immigrant mathematicsteacherswho wereaskedto comparethe teachingandlearning of mathematicsin the formerSovietUnion and Israel-claimed in

her dissertationthat in the formerSovietUnion, unlikein Israel,some learningtechniqueswerethe explicitobjectof instruction. 8 As observedby Ogbu (1992), the statusof "minority" is a doubleedgedsword.As shown by empiricalfindings,belongingto a minority may, in some cases,motivatehardwork and eventualsuccess,whereas in othercasesit mayhavethe oppositeeffect.Immigrants,whom Ogbu calls "voluntaryminorities,"are more likely to belong to the former groupthan arepeoplewhose minoritystatuswas imposedon them. 9 In colloquialRussiandiscourses,the word culture(kultura)is often usedin an evaluative,normativeway, ratherthanto signifya defaultelementof the humancondition. REFERENCES Bakhtin,M. M. (1999). The problemof speechgenres.In A. Jaworski & N. Coupland(Eds.),Thediscursive reader(pp. 121-132). London: Routledge. Bauman,Z. (1996). From pilgrim to tourist-Or a short historyof identity.In S. Hall & P. du Guy (Eds.),Questionsofculturalidentity (pp. 18-36). London:Sage. Beach,K. (1995). Activityas a mediatorof socioculturalchangeandindividualdevelopment:the case of school-worktransitionin Nepal. Mind, Culture,andActivity,2(4), 285-302. Ben-Yehuda,M., Lavy,I., Linchevski,L., & Sfard,A. (in press).Doing wrong with words:What barsstudents'accessto arithmeticaldisin Mathematics course.JournalforResearch Education. and methods. Blumer,H. (1969). Symbolicinteractionism: Perspectives Cliffs: Prentice-Hall. Englewood Cole, M. (1996). Culturalpsychology. Cambridge,MA:BelknapPressof HarvardUniversityPress. Gee, J. P. (2001). Identityas an analyticlens for researchin education. Reviewof Research in Education,25, 99-125. Geertz,C. (1973). Theinterpretation ofcultures.New York:BasicBooks. Gonzalez,N. (1999). Whatwill we do when culturedoes not existanymore?Anthropology and EducationQuarterly, 30, 431-435. Gutierrez,C. D., & Rogoff, B. (2003). Culturalwaysof learning:Individual traits and repertoireof practice.EducationalResearcher, 32(5), 19-25. In S. Hall & P. du Guy (Eds.), Hall, S. (1996). Who needs"identity"? cultural Questionsof identity(pp. 1-18). London:Sage. Hall, S., & du Guy, P. (Eds.).(1996). Questions ofculturalidentity.London: Sage. Harre,R., & Gillett, G. (1995). Thediscursivemind.ThousandOaks, CA: Sage. Hoffman,D. M. (1998). A therapeuticmoment?Identity,self,andculture in the anthropologyof education.Anthropology and Education 29(3), 324-346. Quarterly, Holland,D., & Lave,J. (Eds.).(2001). Historyinperson:Enduringstruggles,contentious practice,intimateidentities.SantaFe, NM: Schoolof AmericanResearchPress;Oxford,UK:JamesCurrey. Holland,D., LachicotteJr.,W., Skinner,D., & Cain, C. (1998). Identityand agencyin culturalworlds.Cambridge,MA: HarvardUniversity Press. Lave,J. (1988). Cognitionin practice.Cambridge,UK:CambridgeUniversityPress.

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AUTHORS ANNA SFARD is Lappan-Phillips-Fitzgerald Professor of Mathematics Education at Michigan State University, and she holds a joint appointment at that university and the University of Haifa. She can be contacted at the University of Haifa, Education, Brazil Building, 304, Haifa 31905, Israel;[email protected]. Focusing on issues related to mathematics education, she investigatesthe implications of the assumption that human thinking is a particular case of communicative activity. ANNA PRUSAK is a lecturer at Oranim Teachers College. She may be contacted at 52 Arlozorov, Haifa 33651, Israel. Her area of specialization is mathematics education. She has taught high school mathematics for many years, first in Gomel, Belarus, and then in Israel. The empirical study presented in this article was implemented as a part of her PhD project.

Manuscriptreceived December 21, 2003 Finalrevision received February21, 2005 Accepted March4, 2005